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Torsion of an arbitrarily shaped nanosized bar

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Abstract

We investigate the Saint-Venant torsion problem of a nanosized bar with arbitrary smooth cross section by enhancing the classical continuum-based model with a theory of surface elasticity based on a version of the Gurtin–Murdoch surface/interface model. An elegant analytical solution is derived by means of conformal mapping, Faber series, Fourier series, and simple matrix algebra. Our solution leads to the establishment of a complex torsion function which, in turn, allows for a concise expression for the torsional rigidity. Our results clearly demonstrate that both the stress field and the normalized torsional rigidity are size dependent. An approximate formula for the size-dependent torsional rigidity is also proposed.

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Acknowledgments

The reviewers’ comments are highly appreciated. This work is supported by the National Natural Science Foundation of China (Grant No: 11272121) and through a Discovery Grant from the Natural Sciences and Engineering Research Council of Canada (Grant No. RGPIN 155112).

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Authors and Affiliations

  1. School of Mechanical and Power Engineering, East China University of Science and Technology, 130 Meilong Road, Shanghai, 200237, China

    Xu Wang

  2. Department of Mechanical Engineering, University of Alberta, 4-9 Mechanical Engineering Building, Edmonton, AB, T6G 2G8, Canada

    Peter Schiavone

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  1. Xu Wang
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  2. Peter Schiavone
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Correspondence to Peter Schiavone.

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Wang, X., Schiavone, P. Torsion of an arbitrarily shaped nanosized bar. Arch Appl Mech 86, 1037–1048 (2016). https://doi.org/10.1007/s00419-015-1077-5

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  • DOI: https://doi.org/10.1007/s00419-015-1077-5

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